Introduction to theory of proportions:
The theory of proportion is one of the basic topic in mathematic. In our usual life, there are a lot of occasions as we compare two quantities by means of their measurements. As soon as we compare two quantities of the same type by division, we contain a ratio of those two quantities.
Definition of Ratio: Ratio means similarity of two like quantities by division.Definition of Theory Proportions:
Proportions is a correspondence of two ratios.
Consider the proportions
a: b = c: d
The first and fourth terms (a and d) are knoen as the extreme terms or extremes.
The second and third terms (b and c) are known as the middle terms or means.
Important property:
Product of extremes = Product of means.
Examples of Theory Proportions:
Let us see some examples of theory of proportions.
Example 1:
Verify 5: 6 = 10: 12 is a proportion or not.
Solution:
Product of extremes = 5*12 = 60
Product of means = 6*10 = 60.
`:.` 60 = 60
These two products are equal.
`:.` 5:6 = 8: 6 is a proportion.
Example 2:
Verify 6: 7 = 12: 15 is a proportion or not.
Solution:
Product of extremes = 6*15 = 90
Product of means = 7*12 = 84
`:.` 90 = 84
These two products are not equal.
So, 6: 7 =12: 15 is not a proportion.
Example 3:
If 2: 3= 6:_ is a proportion, find the missing term.
Solution:
Let us assume the missing value is x
Product of extremes = 2*x
Product of means = 3*6 =18
Since it is a proportion, 2*x =18
2x = 18
Divide both sides by 2 on both sides we get,
2x/2 = 18/2
x = 18/2 = 9
`:. ` The missing term is 9
So the proportion is 2:3 =6: 9
Example 4:
The income and Savings of a family are into the ratio 8: 3 If the income of the family is Rs. 3,300.Find how much is being saved.
Solution:
Let us savings be Rs. x.
`:.` The proportion is 8: 3 = 3300: x
(Income: saving) = (Income: saving)
11x = 9900
11x/11= 9900/11
x= 900
Therefore, the savings = Rs. 900.
No comments:
Post a Comment